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Classical Fourier Transforms : Universitext - Komaravolu Chandrasekharan

Classical Fourier Transforms

Universitext

Paperback

Published: January 1989
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This book gives a thorough introduction on classical Fourier transforms in a compact and self-contained form. Chapter I is devoted to the L1-theory: basic properties are proved as well as the Poisson summation formula, the central limit theorem and Wiener's general tauberian theorem. As an illustraiton of a Fourier transformation of a function "not" belonging to L1 (-, ) an integral due to Ramanujan is given. Chapter II is devoted to the L2-theory, including Plancherel's theorem, Heisenberg's inequality, the Paley-Wiener theorem, Hardy's interpolation formula and two inequalities due to Bernstein. Chapter III deals with Fourier-Stieltjes transforms. After the basic properties are explained, distribution functions, positive-definite functions and the uniqueness theorem of Offord are treated. The book is intended for undergraduate students and requires of them basic knowledge in real and complex analysis.

Contents: Fourier transforms on L1(- , ).- Fourier transforms on L2(- , ).- Fourier-Stieltjes transforms (one variable).- Notes.- References.

ISBN: 9783540502487
ISBN-10: 3540502483
Series: Universitext
Audience: General
Format: Paperback
Language: English
Number Of Pages: 172
Published: January 1989
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 24.41 x 16.99  x 0.99
Weight (kg): 0.3